The quake struck some 125 miles (200 km) from the city of Nikolskoye on Bering Island off the Kamchatka Peninsula.
The epicentre was west of Attu, the westernmost and largest island in the Near Islands group of Alaska's remote Aleutian Islands.
It prompted a tsunami advisory for Alaska's remote Aleutian Islands and the Kamchatka branch of Russia's emergency ministry warned of waves up to 50cm (1-2/2 feet) high could reach Nikolskyoe.
The US Pacific Tsunami Warning Center warned that "hazardous tsunami waves were possible for coasts within 300 km (186 miles) of the earthquake epicenter."
But it later said that based on all available data the tsunami threat from this earthquake had passed.
The earthquake was very shallow, only 6 miles (10 km) below the seabed, which would have amplified its effect, but it was far from any mainland and there were no immediate reports of any casualties or damage.
Waves were later reported as being six inches above tide at sparsely populated Shemya, Alaska, the site of a remote Air Force station in the extreme western Aleutians.
The quake was initially reported as a magnitude 7.7 before being revised down to 7.4 and finally upgraded to 7.8, a major quake normally capable of causing widespread and heavy damage when striking on or near land.
It was followed by numerous aftershocks, including several above magnitude 5.0.
Additional reporting by agencies